interlacing issues on export due to 24 fps software conversion

We are delivering files for distribution and broadcast and are being told there are Interlacing issues particularly in shots with panning or faster motion when viewed on a CRT (interlaced monitor). Unfortunately the majority of these shows are airing in SD via transfer (by a 3rd party) to Beta SP and (without running through a AJA or Matrox box I cannot see the issue on a SD CRT Monitor)

All footage was shot at 24 frames and was then converted to 29.97 using Premiere Pro early on in the post process.

Not necessarily true. The traditional way to bring 24p footage into NTSC broadcast land is to add 3:2 pulldown, which introduces a cadence of three progressive frames followed by two "split" interlaced frames. Premiere Pro can do this automatically, provided that sequence settings are correct. The sequence needs to be a 29.97fps interlaced sequence in order for this to work properly. As long as the field order settings are correct for the format in which you are delivering (upper field first for HD, lower field first for NTSC D1 SD), software "conversion" (adding pulldown) should look identical to hardware conversion. There is no interpolation or blending happening with 3:2 pulldown. Where you might see a difference between hardware and software conversion methods is when cross-converting (720p to 1080i or reverse), downconverting (HD to SD) or standards converting (NTSC to PAL or reverse).

Most likely what is happening is that either your field order was incorrect in your initial Premiere Pro sequence, or the field order was reversed in the subsequent transfer/downconversion to Betacam SP. It's going to be difficult to see what's wrong without viewing the footage on a broadcast monitor fed by proper video output hardware (AJA/Matrox/Blackmagic etc.).

Make sure that your initial conversion is correct - that is, your initial Premiere Pro conversion created 1080i60 footage (29.97fps) with upper field first and 3:2 pulldown. If your footage appears correct up to the point that it was downconverter to SD by the third party, then the issue most likely lies with their conversion method.